This paper aims to address the problem of poor diversity and convergence for traditional evolutionary algorithms in solving multi-objective optimization problems and proposes a cellular differential evolutionary algorithm with double-stage external population-leading. This algorithm divides the maintenance of external population diversity into double stages and introduces new disturbance in the mutation operation to avoid the algorithm falling into a local optimum. In the first stage, the external population is maintained according to the rank and k-nearest neighbor distance. The second stage adopts the external population retention strategy of multi-objective cellular differential algorithm that only retains non-dominated solutions. In both stages, the external population has complete feedback, which means the solutions from the external population randomly replace existing individuals in the two-dimensional grid population after every iteration. Tests on fifteen benchmark functions show that the new algorithm can obtain more uniform Pareto front and competitive convergence results than the other four typical algorithms. Finally, the feasibility and effectiveness of this algorithm are verified by the case study of cycloid speed reducer.

本文旨在解决传统进化算法在解决多目标优化问题时多样性和收敛性差的问题，并提出了一种具有双阶段外部种群主导的细胞差分进化算法。该算法将维持外部种群多样性分为两个阶段，并在变异操作中引入了新的干扰，以避免算法陷入局部最优状态。在第一阶段，根据等级和k最近邻居距离维护外部人口。第二阶段采用多目标细胞差分算法的外部种群保留策略，该策略仅保留非控制解。在两个阶段中，外部人群都有完整的反馈，这意味着每次迭代后，来自外部总体的解决方案会随机替换二维网格总体中的现有个体。对15个基准函数的测试表明，与其他四种典型算法相比，新算法可以获得更统一的Pareto前沿和竞争收敛结果。最后，以摆线针轮减速机为例，验证了该算法的可行性和有效性。